Mathematics discovery applied in Security and algorithms

Recently when learning programming language, I accidentally found out an interesting relationship between prime number and Fibonacci number. There are 3 rules at all for them.

That is, a positive integer number can be analyzed as either:

the sum of a prime number and a Fibonacci number

For example

16 = 11 (prime) + 5 (Fibonnaci)

61 = 59 (prime) + 2 (Fibonacci)

or a prime number minus a Fibonacci number

For example

59 = 61 (prime) – 2 (Fibonacci)

83 = 227 (prime) – 144 (Fibonacci)

or a Fibonacci number minus a prime number

For example

1651=196418 (Fibonacci) – 194767 (Prime)

1759=10946 (Fibonacci) – 9187 (Prime)

By using programming in C and Java, I have tried to prove my finding up to 10,000,000 (10 million). Among them, there are 96,634 records ~ 0.97% failed due to the limitation of great number processing of my programming language (C and Java)

I put all of my 10,000,000 output records in a Microsoft access file Data.accdb, share it with full access in google drive with link